This invention relates, in general, to the coefficient of thermal expansion and, more particularly, to a method for determining the coefficient of thermal expansion.
Matter, hence material, has thermal properties that should be considered when being used to manufacture articles or workpieces. It is important to give serious thought to the thermal conductivity of a material in industries such as the semiconductor industry, the transportation industry, the construction industry, and the garment industry to name a few. For example, in the semiconductor industry it is important to design semiconductor devices to propagate heat away from their junction regions so they don""t undergo a catastrophic thermal failure during operation. Another important thermal property of a material that should be evaluated is the Coefficient of Thermal Expansion (CTE). Still referring to the semiconductor device example, if the semiconductor device includes two thin film materials adjacent to one another and these materials have drastically different Coefficients of Thermal Expansion (CTE""s), the semiconductor device could suffer a catastrophic thermal failure as the device is heated. The failure occurs because one of the two materials expands at a much quicker rate than the other material, thereby creating stresses in both materials which damage one or both of them.
One technique for characterizing the CTE of a material is based on a free body expansion mechanism in which the increase or decrease in volume of the material is proportional to the temperature change. The change in volume of the material caused by the change in temperature is measured using an instrument called a Thermal Mechanical Analyzer (TMA). The volume change is then converted to a CTE value. This technique is used in the xe2x80x9cStandard Test Method for Linear Thermal Expansion of Solid Materials by Thermomechanical Analysis.xe2x80x9d This standard is set forth in ASTM E831-2000. Another technique for characterizing the CTE of a material employs electric resistance strain gages, where a strain gage is bonded to the material to gauge the thermal deformation of the material. This technique is used in the xe2x80x9cStandard Test Method for Linear Thermal Expansion of Rock Using Bonded Electric Resistance Strain Gages.xe2x80x9d This standard is set forth in ASTM D5335-1999. In both of these techniques, the CTE""s are measured under unstressed conditions.
Accordingly, a need exists for a method and an apparatus for measuring the CTE""s of materials under stressed conditions.
The present invention satisfies the foregoing need by providing a method for determining the coefficient of thermal expansion for a specimen. In accordance with an embodiment of the present invention, a specimen or material is equilibrated at a first temperature. A first stress is imparted on the material and then the temperature is changed to a second temperature. The material is equilibrated at the second temperature and a second stress is imparted on the material. The stress change of the material is determined and used to calculate the coefficient of thermal expansion of the material.